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October 6, 2010 10:39
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| <?php | |
| /** | |
| * Taken from PHPExcel | |
| * | |
| * Copyright (c) 2006 - 2009 PHPExcel | |
| * | |
| * This library is free software; you can redistribute it and/or | |
| * modify it under the terms of the GNU Lesser General Public | |
| * License as published by the Free Software Foundation; either | |
| * version 2.1 of the License, or (at your option) any later version. | |
| * | |
| * This library is distributed in the hope that it will be useful, | |
| * but WITHOUT ANY WARRANTY; without even the implied warranty of | |
| * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU | |
| * Lesser General Public License for more details. | |
| * | |
| * You should have received a copy of the GNU Lesser General Public | |
| * License along with this library; if not, write to the Free Software | |
| * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA | |
| * | |
| * @category PHPExcel | |
| * @package PHPExcel_Calculation | |
| * @copyright Copyright (c) 2006 - 2009 PHPExcel (http://www.codeplex.com/PHPExcel) | |
| * @license http://www.gnu.org/licenses/old-licenses/lgpl-2.1.txt LGPL | |
| * @version 1.6.7, 2009-04-22 | |
| */ | |
| define('EPS', 2.22e-16); | |
| define('MAX_VALUE', 1.2e308); | |
| define('LOG_GAMMA_X_MAX_VALUE', 2.55e305); | |
| define('SQRT2PI', 2.5066282746310005024157652848110452530069867406099); | |
| define('XMININ', 2.23e-308); | |
| define('MAX_ITERATIONS', 150); | |
| define('PRECISION', 8.88E-8); | |
| define('EULER', 2.71828182845904523536); | |
| class calculator { | |
| private static $_errorCodes = array( 'null' => '#NULL!', | |
| 'divisionbyzero' => '#DIV/0!', | |
| 'value' => '#VALUE!', | |
| 'reference' => '#REF!', | |
| 'name' => '#NAME?', | |
| 'num' => '#NUM!', | |
| 'na' => '#N/A', | |
| 'gettingdata' => '#GETTING_DATA' | |
| ); | |
| public static function flattenSingleValue($value = '') { | |
| if (is_array($value)) { | |
| $value = self::flattenSingleValue(array_pop($value)); | |
| } | |
| return $value; | |
| } | |
| public static function BETAINV($probability, $alpha, $beta, $rMin=0, $rMax=1) { | |
| $probability = self::flattenSingleValue($probability); | |
| $alpha = self::flattenSingleValue($alpha); | |
| $beta = self::flattenSingleValue($beta); | |
| $rMin = self::flattenSingleValue($rMin); | |
| $rMax = self::flattenSingleValue($rMax); | |
| if ((is_numeric($probability)) && (is_numeric($alpha)) && (is_numeric($beta)) && (is_numeric($rMin)) && (is_numeric($rMax))) { | |
| if (($alpha <= 0) || ($beta <= 0) || ($rMin == $rMax) || ($probability <= 0) || ($probability > 1)) { | |
| return self::$_errorCodes['num']; | |
| } | |
| if ($rMin > $rMax) { | |
| $tmp = $rMin; | |
| $rMin = $rMax; | |
| $rMax = $tmp; | |
| } | |
| $a = 0; | |
| $b = 2; | |
| $maxIteration = 100; | |
| $i = 0; | |
| while ((($b - $a) > PRECISION) && ($i++ < MAX_ITERATIONS)) { | |
| $guess = ($a + $b) / 2; | |
| $result = self::BETADIST($guess, $alpha, $beta); | |
| if (($result == $probability) || ($result == 0)) { | |
| $b = $a; | |
| } elseif ($result > $probability) { | |
| $b = $guess; | |
| } else { | |
| $a = $guess; | |
| } | |
| } | |
| if ($i == MAX_ITERATIONS) { | |
| return self::$_errorCodes['na']; | |
| } | |
| return round($rMin + $guess * ($rMax - $rMin),12); | |
| } | |
| return self::$_errorCodes['value']; | |
| } | |
| public static function BETADIST($value,$alpha,$beta,$rMin=0,$rMax=1) { | |
| $value = self::flattenSingleValue($value); | |
| $alpha = self::flattenSingleValue($alpha); | |
| $beta = self::flattenSingleValue($beta); | |
| $rMin = self::flattenSingleValue($rMin); | |
| $rMax = self::flattenSingleValue($rMax); | |
| if ((is_numeric($value)) && (is_numeric($alpha)) && (is_numeric($beta)) && (is_numeric($rMin)) && (is_numeric($rMax))) { | |
| if (($value < $rMin) || ($value > $rMax) || ($alpha <= 0) || ($beta <= 0) || ($rMin == $rMax)) { | |
| return self::$_errorCodes['num']; | |
| } | |
| if ($rMin > $rMax) { | |
| $tmp = $rMin; | |
| $rMin = $rMax; | |
| $rMax = $tmp; | |
| } | |
| $value -= $rMin; | |
| $value /= ($rMax - $rMin); | |
| return self::incompleteBeta($value,$alpha,$beta); | |
| } | |
| return self::$_errorCodes['value']; | |
| } | |
| private static function betaFraction($x, $p, $q) { | |
| $c = 1.0; | |
| $sum_pq = $p + $q; | |
| $p_plus = $p + 1.0; | |
| $p_minus = $p - 1.0; | |
| $h = 1.0 - $sum_pq * $x / $p_plus; | |
| if (abs($h) < XMININ) { | |
| $h = XMININ; | |
| } | |
| $h = 1.0 / $h; | |
| $frac = $h; | |
| $m = 1; | |
| $delta = 0.0; | |
| while ($m <= MAX_ITERATIONS && abs($delta-1.0) > PRECISION ) { | |
| $m2 = 2 * $m; | |
| // even index for d | |
| $d = $m * ($q - $m) * $x / ( ($p_minus + $m2) * ($p + $m2)); | |
| $h = 1.0 + $d * $h; | |
| if (abs($h) < XMININ) { | |
| $h = XMININ; | |
| } | |
| $h = 1.0 / $h; | |
| $c = 1.0 + $d / $c; | |
| if (abs($c) < XMININ) { | |
| $c = XMININ; | |
| } | |
| $frac *= $h * $c; | |
| // odd index for d | |
| $d = -($p + $m) * ($sum_pq + $m) * $x / (($p + $m2) * ($p_plus + $m2)); | |
| $h = 1.0 + $d * $h; | |
| if (abs($h) < XMININ) { | |
| $h = XMININ; | |
| } | |
| $h = 1.0 / $h; | |
| $c = 1.0 + $d / $c; | |
| if (abs($c) < XMININ) { | |
| $c = XMININ; | |
| } | |
| $delta = $h * $c; | |
| $frac *= $delta; | |
| ++$m; | |
| } | |
| return $frac; | |
| } | |
| private static function incompleteBeta($x, $p, $q) { | |
| if ($x <= 0.0) { | |
| return 0.0; | |
| } elseif ($x >= 1.0) { | |
| return 1.0; | |
| } elseif (($p <= 0.0) || ($q <= 0.0) || (($p + $q) > LOG_GAMMA_X_MAX_VALUE)) { | |
| return 0.0; | |
| } | |
| $beta_gam = exp((0 - self::logBeta($p, $q)) + $p * log($x) + $q * log(1.0 - $x)); | |
| if ($x < ($p + 1.0) / ($p + $q + 2.0)) { | |
| return $beta_gam * self::betaFraction($x, $p, $q) / $p; | |
| } else { | |
| return 1.0 - ($beta_gam * self::betaFraction(1 - $x, $q, $p) / $q); | |
| } | |
| } | |
| private static $logBetaCache_p = 0.0; | |
| private static $logBetaCache_q = 0.0; | |
| private static $logBetaCache_result = 0.0; | |
| private static function logBeta($p, $q) { | |
| if ($p != self::$logBetaCache_p || $q != self::$logBetaCache_q) { | |
| self::$logBetaCache_p = $p; | |
| self::$logBetaCache_q = $q; | |
| if (($p <= 0.0) || ($q <= 0.0) || (($p + $q) > LOG_GAMMA_X_MAX_VALUE)) { | |
| self::$logBetaCache_result = 0.0; | |
| } else { | |
| self::$logBetaCache_result = self::logGamma($p) + self::logGamma($q) - self::logGamma($p + $q); | |
| } | |
| } | |
| return self::$logBetaCache_result; | |
| } | |
| private static $logGammaCache_result = 0.0; | |
| private static $logGammaCache_x = 0.0; | |
| private static function logGamma($x) { | |
| // Log Gamma related constants | |
| static $lg_d1 = -0.5772156649015328605195174; | |
| static $lg_d2 = 0.4227843350984671393993777; | |
| static $lg_d4 = 1.791759469228055000094023; | |
| static $lg_p1 = array( 4.945235359296727046734888, | |
| 201.8112620856775083915565, | |
| 2290.838373831346393026739, | |
| 11319.67205903380828685045, | |
| 28557.24635671635335736389, | |
| 38484.96228443793359990269, | |
| 26377.48787624195437963534, | |
| 7225.813979700288197698961 ); | |
| static $lg_p2 = array( 4.974607845568932035012064, | |
| 542.4138599891070494101986, | |
| 15506.93864978364947665077, | |
| 184793.2904445632425417223, | |
| 1088204.76946882876749847, | |
| 3338152.967987029735917223, | |
| 5106661.678927352456275255, | |
| 3074109.054850539556250927 ); | |
| static $lg_p4 = array( 14745.02166059939948905062, | |
| 2426813.369486704502836312, | |
| 121475557.4045093227939592, | |
| 2663432449.630976949898078, | |
| 29403789566.34553899906876, | |
| 170266573776.5398868392998, | |
| 492612579337.743088758812, | |
| 560625185622.3951465078242 ); | |
| static $lg_q1 = array( 67.48212550303777196073036, | |
| 1113.332393857199323513008, | |
| 7738.757056935398733233834, | |
| 27639.87074403340708898585, | |
| 54993.10206226157329794414, | |
| 61611.22180066002127833352, | |
| 36351.27591501940507276287, | |
| 8785.536302431013170870835 ); | |
| static $lg_q2 = array( 183.0328399370592604055942, | |
| 7765.049321445005871323047, | |
| 133190.3827966074194402448, | |
| 1136705.821321969608938755, | |
| 5267964.117437946917577538, | |
| 13467014.54311101692290052, | |
| 17827365.30353274213975932, | |
| 9533095.591844353613395747 ); | |
| static $lg_q4 = array( 2690.530175870899333379843, | |
| 639388.5654300092398984238, | |
| 41355999.30241388052042842, | |
| 1120872109.61614794137657, | |
| 14886137286.78813811542398, | |
| 101680358627.2438228077304, | |
| 341747634550.7377132798597, | |
| 446315818741.9713286462081 ); | |
| static $lg_c = array( -0.001910444077728, | |
| 8.4171387781295e-4, | |
| -5.952379913043012e-4, | |
| 7.93650793500350248e-4, | |
| -0.002777777777777681622553, | |
| 0.08333333333333333331554247, | |
| 0.0057083835261 ); | |
| // Rough estimate of the fourth root of logGamma_xBig | |
| static $lg_frtbig = 2.25e76; | |
| static $pnt68 = 0.6796875; | |
| if ($x == self::$logGammaCache_x) { | |
| return self::$logGammaCache_result; | |
| } | |
| $y = $x; | |
| if ($y > 0.0 && $y <= LOG_GAMMA_X_MAX_VALUE) { | |
| if ($y <= EPS) { | |
| $res = -log(y); | |
| } elseif ($y <= 1.5) { | |
| // --------------------- | |
| // EPS .LT. X .LE. 1.5 | |
| // --------------------- | |
| if ($y < $pnt68) { | |
| $corr = -log($y); | |
| $xm1 = $y; | |
| } else { | |
| $corr = 0.0; | |
| $xm1 = $y - 1.0; | |
| } | |
| if ($y <= 0.5 || $y >= $pnt68) { | |
| $xden = 1.0; | |
| $xnum = 0.0; | |
| for ($i = 0; $i < 8; ++$i) { | |
| $xnum = $xnum * $xm1 + $lg_p1[$i]; | |
| $xden = $xden * $xm1 + $lg_q1[$i]; | |
| } | |
| $res = $corr + $xm1 * ($lg_d1 + $xm1 * ($xnum / $xden)); | |
| } else { | |
| $xm2 = $y - 1.0; | |
| $xden = 1.0; | |
| $xnum = 0.0; | |
| for ($i = 0; $i < 8; ++$i) { | |
| $xnum = $xnum * $xm2 + $lg_p2[$i]; | |
| $xden = $xden * $xm2 + $lg_q2[$i]; | |
| } | |
| $res = $corr + $xm2 * ($lg_d2 + $xm2 * ($xnum / $xden)); | |
| } | |
| } elseif ($y <= 4.0) { | |
| // --------------------- | |
| // 1.5 .LT. X .LE. 4.0 | |
| // --------------------- | |
| $xm2 = $y - 2.0; | |
| $xden = 1.0; | |
| $xnum = 0.0; | |
| for ($i = 0; $i < 8; ++$i) { | |
| $xnum = $xnum * $xm2 + $lg_p2[$i]; | |
| $xden = $xden * $xm2 + $lg_q2[$i]; | |
| } | |
| $res = $xm2 * ($lg_d2 + $xm2 * ($xnum / $xden)); | |
| } elseif ($y <= 12.0) { | |
| // ---------------------- | |
| // 4.0 .LT. X .LE. 12.0 | |
| // ---------------------- | |
| $xm4 = $y - 4.0; | |
| $xden = -1.0; | |
| $xnum = 0.0; | |
| for ($i = 0; $i < 8; ++$i) { | |
| $xnum = $xnum * $xm4 + $lg_p4[$i]; | |
| $xden = $xden * $xm4 + $lg_q4[$i]; | |
| } | |
| $res = $lg_d4 + $xm4 * ($xnum / $xden); | |
| } else { | |
| // --------------------------------- | |
| // Evaluate for argument .GE. 12.0 | |
| // --------------------------------- | |
| $res = 0.0; | |
| if ($y <= $lg_frtbig) { | |
| $res = $lg_c[6]; | |
| $ysq = $y * $y; | |
| for ($i = 0; $i < 6; ++$i) | |
| $res = $res / $ysq + $lg_c[$i]; | |
| } | |
| $res /= $y; | |
| $corr = log($y); | |
| $res = $res + log(SQRT2PI) - 0.5 * $corr; | |
| $res += $y * ($corr - 1.0); | |
| } | |
| } else { | |
| // -------------------------- | |
| // Return for bad arguments | |
| // -------------------------- | |
| $res = MAX_VALUE; | |
| } | |
| // ------------------------------ | |
| // Final adjustments and return | |
| // ------------------------------ | |
| self::$logGammaCache_x = $x; | |
| self::$logGammaCache_result = $res; | |
| return $res; | |
| } | |
| } |
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